9x^2(2x+7)-12x(2x+7)=3x(2x+7)(3x-4) ...at the end where did the (3x-4) come from?

- anonymous

9x^2(2x+7)-12x(2x+7)=3x(2x+7)(3x-4) ...at the end where did the (3x-4) come from?

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- schrodinger

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- amistre64

As far as I can tell; you typed it in there. :)

- anonymous

It's on the website where I found this openstudy group. I never answered it. It says that's the answer and I'm a bit confused.

- amistre64

You have 2 numbers that are the same (2x+7) and (2x+7); so factor those out and your left with:
(2x+7) (9x^2-12x) does this make sense?
Now, we can factor (9x^2 -12x) even further to get:
3x (x-4) ; it should be:
(3x) (2x+7) (x-4). It would be a typo :)

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## More answers

- amistre64

ack!! my mistake
3x(3x-4) is correct... do you know why?

- anonymous

No, I don't know why. xD I have a math 11 test tomorrow and I'm a bit nervous. I can't get the hang of this stuff. :/ Mind explaining?

- amistre64

do you understand the first step....how to factor out (2x+7) and get left with (9x^2 -12x)? It is the opposite of distirbuting...

- anonymous

The question is 9x^2(2x+7)-12x(2x+7) and I know that theres a 3x in each term and a (2x+7) so you can factor those out right? So on the site it says it equals 3x(2x+7)(3x-4) and I understand how I got the 3x(2x+7) because both terms have it, but I'm so lost as to where the 3x-4 came up.

- amistre64

lets take it step by step and you will see where it comes from...fair enough?

- anonymous

Kay. :)

- amistre64

9x^2(2x+7)-12x(2x+7) has a common factor that is blaringly obvious. It is (2x+7) right? just let me know if this is correct....

- anonymous

Yes, but doesn't it have 3x as well?

- amistre64

3x doesnt matter yet; it will come, but not yet. lets clean it up some first ok?

- anonymous

kk, so yes, 2x+7

- amistre64

when we factor out (2x+7) are we left with:
(2x+7) (9x^2 -12x) ? yes or no...

- amistre64

think of (2x+7) call it A if you have to..

- anonymous

yes, we're left with it.

- anonymous

sorry i'm talkign long to reply. keep pressing enter instead of post.

- anonymous

taking.*

- amistre64

its ok...
Now we can factor (9x^2 -12x). Do you see how we could do that?

- anonymous

Oh wait! So, you can take out a 3 because of 9 and 12, and you can also take out an x, hence 3x, and you can get a 4 because 3X4 = 12.

- amistre64

you are brilliant :)

- anonymous

So 3x(3-4)

- anonymous

So once we get that we just put the 2x+7 back in?

- anonymous

And our 3x would go in front.

- amistre64

3x(3x - 4) = 9x^2 -12x right?

- amistre64

but yes, you can put the numbers back in whatever order you feel comfortable with.

- anonymous

yes! :D

- anonymous

So that's why there was a 4. I was confused about that but now I get it, because of the 3-4, 3x4= 12. Makes so much more sense now.

- amistre64

Just remember to take things step-by-step and it should all work out :)

- anonymous

I'm still bad at this stuff, though. I understand that question, but there's like 4 different types of facorting we're doing in class and I get confused when I'm doing problems because I'm not sure which one I'm supposed to use.

- amistre64

I hate the way they teach factoring in school. Because there is only one method that you actually use.. it is to "un" distribute or take apart; what was already put together.

- anonymous

& my math teacher picks favorites, if you're not up there in your math grades then he'll get mad. It's really annoying. I failed my past two math tests. I had 88 on my first test, but when he started teaching I dropped down to half that mark, to like 44. Tomorrow's test is kinda crucial.

- amistre64

what factoring methods do you need help with?

- anonymous

I'm strong in every other subject besides math. Anyways, care to help me with a couple more problems?

- anonymous

I'll list a problem I was having trouble with today. One second, I'll find it in my book.

- anonymous

x^2+8x+12
x^2+3x-18
and it's supposed to be over each other.

- anonymous

The top part = (x+2)(x+3) right?

- amistre64

glorified fractions is all that is.
The equation gives you clues as to what to do. Do you see the "sign" of the last term?

- anonymous

What sign? I'm not sure what you mean by that, sorry.

- amistre64

(+12) OR (-18)
the last term is gotten by multipying 2 numbers together.
What combination of "signs" when multiplied give you a (+) answer?
What combination of "signs" when multiplied give you a (-) answer?
Can you tell me?

- anonymous

two positives = positive, two negatives = positive, and a - and a + = a -, right?

- amistre64

thats right. So the last term gives us a clue about our middle term. Becuase the middle term takes those same 2 numbers and adds them together.
Lets focus on the top: +8 +12.
we need 2 numbers that are either (-)(-) or (+)(+) to get the (+12) right?
and they need to add together to get a (+) for the middle term (+8).
Does this make sense?

- anonymous

Yeah that makes sense, we're trying to get a LCD?

- anonymous

2 and 6?

- amistre64

we will soon enough; but lets take it step by step.
We can start to set up our answer like this: Good now...
(x 2 ) (x 6 ) what "sign" do we need to use to fill this in? to get a (+12) and a (+8)

- anonymous

+

- amistre64

Yes, (x+2) (x+8) is the answer for the top; store it away somewhere where it wont get broken...

- amistre64

opps... make that (x+2)(x+6) and feel free to correct me :)

- anonymous

That's the answer for the top? Don't the 6 break down to a 3? Or we can't do that because we're only going half of 12?

- amistre64

there is nothing that x and 6 have in common so it is as far as it will go. to double check, multiply them back together.

- anonymous

I understand.

- amistre64

x^2 +3x -18 the last term tells us what signs we need to use. and the middle term tells us which of those signs gets the bigger number. Does that make sense?

- amistre64

what makes a (-) when multiplied together?

- anonymous

+ and -

- anonymous

I don't know what you mean by which sign gets the bigger number, though.

- amistre64

good; then its our only option:
(x+ )(x- ) is what we are dealt. now find 2 numbers that multiply to 18 and "subtract" to get 3.
Do you see why we need the (+)number to be bigger than the (-)number to get (+3)?

- anonymous

I'm a bit confused.

- amistre64

the numbers are gonna be 6 and 3... to equal 18 right?
-6 +3 = -3
+6 -3 = +3
do you see it?

- anonymous

I thought we were trying to equal 18? Not - and +3?

- anonymous

-3*

- amistre64

ok...we can do that as well; what are the factors of 18 that subtract to get (+3) for a middle term?
1 and 18
2 and 9
3 and 6
thats it... right?

- anonymous

yep

- amistre64

one number has to be (-) and the other number has to (+)
In order to get the (+3) for the middle term, the largest number has to be (+)
such as: +6 -3 = +3
and +6 times -3 equals -18
does this make sense?

- anonymous

yes, it does!

- amistre64

then we can fill in our stuff now:
(x +6) (x -3) is our answer. for the bottom.
Can we cross anything out from top to bottom that are alike?

- anonymous

x+6

- amistre64

Good, and we are left with:
(x+2)(x+6) (x+2)
---------- = -----
(x+6)(x-3) (x-3)

- anonymous

so then it's gonna be x+2 over x+3

- anonymous

haha yep!

- anonymous

wait, -3

- anonymous

thats what I had written down on paper, typo on here. lol.

- amistre64

i wish I had time for more, but my macroeconomics class is starting and running for the next 2 hours.
You can do this, it is really stuff you already know :)

- anonymous

Thanks for your help, and perfect timing. I have to go right now too.

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